An uncountable countable set
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From: Virgil on 26 Oct 2006 17:06 In article <4540d27e(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > The vase becomes empty in the usual way, by having everything in it > > removed. And the time at which that finally has occurred is noon. > > Nothing is removed at noon. By noon, everything has already ben removed. > > > > > The only relevant question is "According to the rules set up by the > > problem, is each ball inserted before noon also removed before noon?" > > > > An affirmative answer confirms that the vase is empty at noon. > > A negative answer directly violates the conditions of the problem. > > > > How does TO answer? > > That you are a broken record, and noon does not exist in the experiment. As every action is timed in relation to noon, if noon doesn't happen, nothing happens. > > It is never the case that every ball inserted has been removed. Then TO is caught in a time warp, because it happens everywhere else.
From: Virgil on 26 Oct 2006 17:08 In article <4540d345(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <453fb693(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> David Marcus wrote: > >>> Virgil wrote: > >>>> In article <453e824b(a)news2.lightlink.com>, > >>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>> Virgil wrote: > >>>>>> In article <453e4a85(a)news2.lightlink.com>, > >>>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>>>> If the vase exists at noon, then it has an uncountable number of > >>>>>>> balls > >>>>>>> labeled with infinite values. But, no infinite values are allowed i > >>>>>>> the > >>>>>>> experiment, so this cannot happen, and noon is excluded. > >>>>>> So did the North Koreans nuke the vase before noon? > >>>>>> > >>>>>> The only relevant issue is whether according to the rules set up in > >>>>>> the > >>>>>> problem, is each ball inserted before noon also removed before noon?" > >>>>>> > >>>>>> An affirmative confirms that the vase is empty at noon. > >>>>>> A negative directly violates the conditions of the problem. > >>>>>> > >>>>>> How does TO answer? > >>>>> You can repeat the same inane nonsense 25 more times, if you want. I > >>>>> already answered the question. It's not my problem that you can't > >>>>> understand it. > >>>> It is a good deal less inane and less nonsensical than trying to > >>>> maintain, as TO and his ilk do, that a vase from which every ball has > >>>> been removed before noon contains any balls at noon that have not been > >>>> removed. > >>> Ah, you are forgetting the balls labeled with "infinite values". Those > >>> balls haven't been removed before noon. Although, I must say I'm not too > >>> clear on when they were added. > >>> > >> At noon > > > > Where in the original problem does it say anything like that? > > It doesn't. It specifically excludes noon as a time in the experiment by > specifying that all balls are finitely numbered and all events are > finitely before noon. Duh. How can there be a before without what comes after? How can there be a before noon without a noon? Does God cause the sun to stand still and stop time?
From: MoeBlee on 26 Oct 2006 17:12 Lester Zick wrote even more sheer brilliance! It starts with: > On 25 Oct 2006 17:32:25 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: and ends with: > ~v~~ and, veritably, every word in between is magnificence. I won't quote more that opening and close, as one can become overwhelmed by so much wisdom from just one man in just one day. MoeBlee
From: Virgil on 26 Oct 2006 17:12 In article <4540d449(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > MoeBlee wrote: > > Tony Orlow wrote: > >>> But none of Robinson's non-standard numbers are cardinalities. > >> No kidding. They actually make sense. > > > > You said you have not properly studied chapter II in the book - the one > > that includes mathematical logic, model theory, and set theory (does it > > not? I'll stand corrected if it doesn't). What are you going to say > > when you find out that what you say makes sense rests on a foundation > > of set theory that you say doesn't make sense? Or, if I'm incorrect > > that Robinson's work in non-standard analysis doesn't presuppose basic > > mathematical logic, model theory, and set theory, then I'll benefit by > > being corrected in my admittedly cursory understanding of the matter. > > > > MoeBlee > > > > Uh, if Robinson's thesis is built upon transfinite set theory, then that > is evidence right there that it's inconsistent, since you have a > smallest infinity, omega, but Robinson has no smallest infinity. Apples versus oranges. Robinson's non-principle ultrafilters cannot exist without an omega. > Robinson doesn't use ordinals or cardinals that I've seen. Then you skipped that part. Without them he cannot build the ultrafilters on which is theory rests.
From: Virgil on 26 Oct 2006 17:17
In article <4540d710(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David Marcus wrote: > >> So, when does the vase become empty, > > > > At noon. > > When nothing happens? What balls are removed at noon? Can the vase > become empty by a means other than ball removal? By means of all balls being removed. > > There are balls at every moment before noon, nothing happens at noon, > but they are all gone suddenly? They are gone one by one before noon. > > What causes the vase to be empty at noon, if not removals at noon, which > cannot occur? By removals before noon which have occurred. |